Abstract
Ground-state properties of a few spin- 1 / 2 ultra-cold fermions confined in a one-dimensional trap are studied by the exact diagonalization method. In contrast to previous studies, it is not assumed that the projection of a spin of individual particles is fixed. Therefore, the spin is treated as an additional degree of freedom and the global magnetization of the system is established spontaneously. Depending on the shape of the trap, inter-particle interactions, and an external magnetic field, the phase diagram of the system is determined. It is shown that, for particular confinements, some values of the magnetization cannot be reached by the ground-state of the system.
Highlights
Recent ground-breaking experiments on ultra-cold atoms confined in quasi-one-dimensional optical traps have opened a completely new avenue for studying problems of a few quantum particles [1–4]
It becomes possible to control mutual interactions and the external confinement that the particles are stored in and to control the number of particles in experiments repeated with tremendous accuracy [5–8]
We focus on the total magnetization of the interacting system, which is established spontaneously in response to the external confinement and the magnetic field
Summary
Recent ground-breaking experiments on ultra-cold atoms confined in quasi-one-dimensional optical traps have opened a completely new avenue for studying problems of a few quantum particles [1–4]. In the context of mixtures of a few interacting ultra-cold fermions, it is assumed that particles from different components belong to different, fundamentally distinguishable, families [19,20] This assumption is well justified from the experimental point of view since different fermionic components are usually formed from different atomic elements [21–26] or from atoms belonging to different irreducible spin representations [7,15,27–33]. In such a case, particles are forbidden to change their flavor, and, as a consequence, the number of particles of a given type is conserved
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